code: def integrate_kde(self, other):
      if other.d != self.d:
          raise ValueError("KDEs are not the same dimensionality")
  
      chol = linalg.cho_factor(self.covariance + other.covariance)
      norm = jnp.sqrt(2 * np.pi) ** self.d * jnp.prod(jnp.diag(chol[0]))
      norm = 1.0 / norm
  
      sm, lg = (self, other) if self.n < other.n else (other, self)
      result = vmap(
          partial(
              _gaussian_kernel_convolve,
              chol,
              norm,
              lg.dataset,
              lg.weights,
          ),
          in_axes=1,
      )(sm.dataset)
      return jnp.sum(result * sm.weights)
  
imports: from dataclasses import dataclass
  from functools import partial
  from typing import Any
  import numpy
  import scipy.stats
  import jax.numpy
  from jax import jit, lax, random, vmap
  from jax._src.numpy.util import check_arraylike, promote_dtypes_inexact, _wraps
  from jax._src.tree_util import register_pytree_node_class
  from jax.scipy import linalg, special
label_desc: Use image node_id 11 for calling the gaussian_kde obj's underlying member method code with example usage: obj.integrate_kde(other) and returns: jnp